Four new hotspots, expected to be switched on by June, will include the Smart Street Mall and Pinjarra Road.
The company set up a pop-up stall on Mandurah Terrace last week so the community could ask questions.
Telstra group executive of retail Gordon Ballantyne said the trial of four existing hotspots along Mandurah Terrace had exceeded expectations.
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READ NOWMr Ballantyne said expansion of the network was another important step towards Telstra meeting an ambitious goal to roll out Australia's biggest Wi-Fi network with 1500 new hotspots across Australia by June.
"Now we want the community to help us create a Wi-Fi service that connects them to the places where they love spending time " shopping precincts, popular recreation spaces or their favourite cafe strip, he said.
Four hotspots have already been live since December and so far 223GB of data has been downloaded free.
The Mandurah hotspots are free during the trial period, which continues until June. When the full network is launched, Australians will be able to access the full network in several ways:
n Telstra home broadband customers with a compatible broadband service and gateway who join can use their home broadband allowance at thousands of domestic hotspots.
n Members will also be able to use their home broadband allowance overseas by connecting to more than 14 million Fon-enabled hotspots around the world.
n Non-Telstra customers and Telstra customers who have not joined the Wi-Fi community will be able to connect to Fon-enabled Telstra WI-FI-hotspots for a small charge using guest passes.